Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the
ultraviolet, as initially noted by Horava, but are increasingly constrained in the infrared. At low energies, ˇ
Horava gravity is characterized by three dimensionless couplings, ˇ α, β and λ, which vanish in the
general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings
(α and β) to tiny values, but the third remains relatively unconstrained (0 ≤ λ ≲ 0.01–0.1). Moreover,
demanding that (slowly moving) black-hole solutions are regular away from the central singularity
requires α and β to vanish exactly. Although a canonical constraint analysis shows that the class of
khronometric theories resulting from these constraints (α 1⁄4 β 1⁄4 0 and λ ≠ 0) cannot be equivalent to
General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary
pulsars and gravitational-wave generation show perfect agreement with general relativity. Here, we
analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave
exactly as in general relativity, as far as observational predictions are concerned. Nevertheless, we find
that spherical collapse leads to the formation of a regular universal horizon, i.e., a causal boundary for
signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons.
Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2
graviton of general relativity remains strongly coupled at low energies, even on curved backgrounds.
These puzzling results suggest that any further bounds on Horava gravity will probably come from ˇ
cosmology.
